基于多项式展开的三角平动点垂直周期轨道解析构建方法研究

平动点是圆型限制性三体问题中的五个平衡解,其附近存在着大量的周期轨道,研究这些周期轨道的构建方法在深空探测中具有重要的理论及工程意义.本文从模态运动的角度出发,分析三角平动点附近周期轨道,通过多项式展开法构建出主坐标下周期轨道三个运动方向之间的渐近关系,从新的角度分析了系统的动力学特性和三维周期运动三个方向内在关联以及物理规律.同时可以为设计真实力学模型下的飞行器轨道提供借鉴.文中提出的方法可以被拓展至椭圆型限制性三体问题的三维周期轨道构建或共线平动点附近的轨道构建中.     

A novel method of periodic orbit computation in circular restricted three-body problem

Periodic orbits are fundamental keys to understand the dynamical system of circular restricted three-body problem, and they play important roles in practical deep-space exploration. Current methods of periodic orbit computation need a high-order analytical approximate solution to start the iteration process, thus making the computation complicated and limiting the types of periodic orbits that can be obtained. By utilizing the symmetry of the restricted three-body problem, a special kind of flow function is...